A Canon of Probabilistic Rationality

TL;DR

This paper characterizes probabilistic rationality by linking Luce's Choice Axiom with the Weak Axiom of Revealed Preference, showing that random choice can be viewed as a tie-breaking among optimal alternatives.

Contribution

It provides a formal proof that Luce's Choice Axiom is equivalent to a probabilistic extension of the Weak Axiom, clarifying the foundation of probabilistic choice models.

Findings

Luce's Choice Axiom corresponds to a probabilistic version of the Weak Axiom.

Random choice is modeled as tie-breaking among optimal alternatives.

The result formalizes Luce's view of probabilistic rationality.

Abstract

We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice then occurs according to a tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom. Our result shows that the Choice Axiom is, in a precise formal sense, a probabilistic version of the Weak Axiom. It thus supports Luce's view of his own axiom as a "canon of probabilistic rationality."